## Expected value and variance of probability distribution

Expectation and variance of Prob. Dist | ||
---|---|---|

Values of $X$ (Separated by comma ,) | ||

Probabilities $P_x$ (Separated by comma ,) | ||

Results | ||

Expected value of $X$: $E(X)$ | ||

Variance of $X$: $\sigma^2$ | ||

Standard deviation of $X$: $\sigma$ | ||

## Formula

`$E(X) =\mu = \sum_x x*P(X=x)$`

`$V(X) =\sigma^2 = E(X^2) -[E(X)]^2$`

where `$E(X^2) = \sum_x x^2*P(X=x)$`